Subresultants and generic monomial bases

Given $n$ polynomials in $n$ variables of respective degrees $d_1,\dots ,d_n$, and a set of monomials of cardinality $d_1?d_n$, we give an explicit subresultant-based polynomial expression in the coefficients of the input polynomials whose non-vanishing is a necessary and sufficient condition for this set of monomials to be a basis of the ring of polynomials in $n$ variables modulo the ideal generated by the system of polynomials. This approach allows us to clarify the algorithms for the Bézout construction of the resultant.